Single-image Specular Reflection Separation

ABSTRACT

Systems and methods are discussed to separate the specular reflectivity and/or the diffuse reflectivity from an input image. Embodiments of the invention can be used to determine the specular chromaticity by iteratively solving one or more objective functions. An objective function can include functions that take into account the smooth gradient of the specular chromaticity. An objective function can take into account the interior chromatic homogeneity of the diffuse chromaticity and/or the sharp changes between chromaticity. Embodiments of the invention can also be used to determine the specular chromaticity of an image using a pseudo specular-free image that is calculated from the input image and a dark channel image that can be used to iteratively solve an objective function(s).

RELATED APPLICATIONS

The present application claims priority to, and is a divisionalapplication of, U.S. application Ser. No. 13/859,468 for “Single-ImageSpecular Reflection Separation” filed Apr. 9, 2013, now allowed, whichis incorporated by reference herein in its entirety.

FIELD

This disclosure relates generally to image processing.

BACKGROUND

The observed color of an image is formed from the spectral energydistributions of the light reflected by the surface reflectance, and theintensity of the image color is determined by the imaging geometry.Diffuse reflection can be assumed to be associated only with therelative angle between the light direction and the surface normal in theimaging geometry regardless of the viewing direction. Specularreflection, on the other hand, is dependent on the viewing direction.This viewing dependency of the specular reflection can lead to problemsin many computer vision applications such as stereo matching,segmentation, and/or recognition.

Stereo matching extracts of 3D information from digital images bycomparing information about a scene from two vantage points. Becausespecular reflection changes depending on the view point, if one of thetwo images under comparison to extract 3D information includes specularreflections and the other does not, large intensity differences may bepresent. This can lead to miscalculations of 3D information from thesetwo images. Despite this potential for error, it is common to assumethat specular reflections do not exist in the images.

Image segmentation is the process of assigning a label to every pixel inan image such that pixels with the same label share certain visualcharacteristics. A specular reflection within an image shows thereflection rather than the object upon which the reflection occurs. Assuch the color and/or intensity of pixels representing the specularreflection may not be labeled with the object, which is the object ofimage segmentation. This can lead to pixels being mislabeled orsegmented. Similar problems can occur in image recognition techniques.

Most applications simply consider the observed image as a diffusereflection model and disregard the specular reflection componentsbecause they are considered outliers.

SUMMARY

Embodiments of the invention include a method for determining thespecular reflectivity within an input image. Embodiments of theinvention can include receiving an input image at a computer devicethat. The input image can include a red channel, a green channel, and ablue channel for each pixel in the input image. A dark channel image canbe calculated from the input image. The dark channel image can comprisean image for each pixel value having the lowest pixel value of thecorresponding red channel pixel, green channel pixel, and blue channelpixel of the input image. A pseudo specular-free image can be calculatedas the difference between the input image and the dark channel image. Aspecular chromaticity of the input image can be determined from thepseudo specular-free image, which can be returned.

Embodiments of the invention can also receive an input image at acomputer device. The input image can include a red channel, a greenchannel, and a blue channel for each pixel in the input image. A clusteranalysis can be performed on the input image that clusters each pixel inthe input image into clusters having similar chromaticity. The clusteranalysis can determine a chromaticity index for each pixel and achromaticity vector that indicates the average chromaticity of eachcluster represented by the index. An objective function can then besolved to determine the specular reflectivity of the input image. Thisobjective function can have a number of properties. For example, theobjective function can include a function that specifies that thespecular reflectivity is smooth across edges within the input image. Asanother example, the objective function can specify that the diffusereflectivity is relatively constant for the same chromaticity. Asanother example, the objective function can specify that the diffusereflectivity is relatively constant within each cluster. As yet anotherexample, the objective function can specify that the diffusereflectivity changes sharply between clusters. As yet another example,the objective function can specify a combination of any of these orother objective functions. The specular reflectivity of the input imagecan then be returned.

These illustrative embodiments are mentioned not to limit or define thedisclosure, but to provide examples to aid understanding thereof.Additional embodiments are discussed in the Detailed Description, andfurther description is provided there. Advantages offered by one or moreof the various embodiments may be further understood by examining thisspecification or by practicing one or more embodiments presented.

BRIEF DESCRIPTION OF THE FIGURES

These and other features, aspects, and advantages of the presentdisclosure are better understood when the following Detailed Descriptionis read with reference to the accompanying drawings.

FIGS. 1A, 1B and 1C show a synthetic image and its diffuse and specularcomponents generated to illustrate various embodiments of the invention.

FIGS. 2A and 2B show a photograph of fruit representing diffuse andspecular components of a real image.

FIGS. 3A and 3B show pseudo specular images calculated usingconventional techniques and embodiments of the invention.

FIG. 4 is a flowchart of a process for determining the specularchromaticity from an image according to some embodiments of theinvention.

FIGS. 5A and 5B show results of the specular and diffuse reflectivitycalculated from FIG. 1A using various embodiments of the invention.

FIGS. 6A, 6B, 6C, and 6D show an input image, an image representing thespecular chromaticity using embodiments of the invention, a dark channelimage created from the input image using embodiments of the image, andan image representing the specular chromaticity using conventionaltechniques respectively.

FIGS. 7A, 7B and 7C show an input image and the specular layercalculated using conventional techniques and embodiments of theinvention.

FIGS. 8A, 8B and 8C show an input image and the specular layercalculated using conventional techniques and embodiments of theinvention.

FIGS. 9A, 9B and 9C show an input image and the specular layercalculated using conventional techniques and embodiments of theinvention.

FIG. 10 shows an illustrative computational system for performingfunctionality to facilitate implementation of embodiments describedherein.

DETAILED DESCRIPTION

Systems and methods are disclosed to separate the specular reflectivityand the diffuse reflectivity from an input image. Images are arepresentation of light reflected off objects framed within the image.The reflected light captured in an image can either be from a diffusereflection or a specular reflection. It has proven challenging toaccurately distinguish between diffuse reflection and specularreflection. Because diffuse reflections make up the majority of thelight in an image and noting that challenges exist in separating thetwo, most image processing applications assume all the light in an imageis diffuse.

In some embodiments of the invention, the chromaticity of an image canbe analyzed. The chromaticity of an image represents the color of theimage (or even a pixel) regardless of the brightness (or luminance) ofthe image. Hence, it can be assumed that the diffuse chromaticity of animage can represent the true (or inherent) color of a surface, and thespecular chromaticity can represent the true (or inherent) illuminationof the surface. Thus, an image can be separated into the diffusechromaticity and the specular chromaticity.

FIGS. 1A, 1B and 1C show an example of how an image can be separatedinto diffuse and specular portions. FIG. 1A shows an image created fromthe diffuse chromaticity shown in FIG. 1B and the specular chromaticityshown in FIG. 1C. FIG. 1B shows the diffuse chromaticity component ofthe image, which when compared with FIG. 1C includes all the colorinformation. In particular, this image shows two vertical panels withseparate and distinct colors. FIG. 1C shows the specular chromaticitycomponent of the image, which represents illumination and is agnosticregarding color (hence the grayscale image). FIG. 1A is the linearcombination of FIG. 1B and FIG. 1C.

FIG. 2A is a photograph of a lemon, pear and apple. In this imagespecular reflection 205 is shown by the glare reflected off each pieceof fruit or the shiny reflection. The specular reflections are a smallportion of the entire image. The apple, in particular, shows a strongspecular reflection. Because it is such a minor aspect of the image, itcan be common to ignore the contribution of the specular reflections.But doing so risks misunderstanding the objects in the image. As notedabove, it can be seen in this image that the diffuse reflectivitycaptured in this image represents the true color of the fruit in theimage.

FIG. 2B shows the specular reflection layer of FIG. 2A created usingembodiments of the invention. As shown in the image, only the portionsof the image representing the specular reflections (e.g., specularreflection 205) show up in this image.

Embodiments of the invention can be used on any image.

Techniques and systems are disclosed herein for determining orestimating the specular chromaticity, the diffuse chromaticity, or bothfrom an input image. Embodiments of the invention can be used todetermine the specular chromaticity by iteratively solving one or moreobjective functions.

Objective functions are commonly used in optimization problems. Anobjective function can be defined to represent various conditions orparameters that exist in specular and/or diffuse reflectivities. Bysetting up an objective function that represents a linear combination ofa number of conditions or parameters, the relative contribution of eachof these conditions or parameters can be determined. Using any number ofoptimization techniques, an objective function can be maximized orminimized by systematically choosing input values and then computing thevalue of the function. The following describes the reasoning behind theselection of an exemplary objective function. An exemplary simplifiedobjective function and initialization parameters are described.

In some embodiments one component of the objective function(s) can bechosen to represent the smooth gradient of the specular chromaticity. Asshown in FIG. 1C, the specular chromaticity changes smoothly across theimage; there are no abrupt changes in the specular chromaticity.

Moreover, a portion of the objective function can be chosen to take intoaccount the interior chromatic homogeneity of the diffuse chromaticityand/or the sharp changes between chromaticity. This is shown in FIG. 1B,where the chromaticity (or color) of each vertical panel is homogeneouswithin the boundaries of the panel. Yet, at the line where the colorchanges from one chromaticity to the other, this change occurs abruptly.Examples of objective functions that take into account these featuresare described in detail below.

Embodiments of the invention can determine the specular chromaticity ofan image using a pseudo specular-free image that is calculated from theimage and a dark channel image, which is a composite image from the red,green and blue channels of the image and is described in detail below.Typically, each frame is defined as a mix of red, green and blue colors.Each pixel, therefore, can be represented as a linear combination ofred, green, and blue values. These different values are often calledchannels such as the red channel, the blue channel, and the greenchannel. This pseudo specular-free image can be used to iterativelysolve one or more objective functions. Each pixel of the dark channelimage can have for each pixel value the lowest pixel value of thecorresponding red channel pixel, green channel pixel, and blue channelpixel. In some embodiments, this pseudo specular-free image can preservecolor boundaries (chromaticity clusters) and/or can improve results whencolor channels are ambiguous in saturation values.

An input image I(x) can include red, blue and green channels. As notedabove the reflectivity of the input image I(x) can be considered acombination of the diffuse, I_(d)(x), and specular layers, I_(s)(x):

I(x)=I _(d)(x)+I _(s)(x).   (1)

This is shown in FIG. 1A where the image is a combination of the diffuseimage shown in FIG. 1B and the specular image shown in FIG. 1C.

In some embodiments the chromaticity of an image can be represented as anormalized color vector. The normalized color vector, for example, canrepresent each pixel for each channel as the pixel value divided by thesum of all pixel values in the channel:

$\begin{matrix}{{{\overset{\sim}{I}(x)} = \frac{I(x)}{\sum\limits_{c \in {\{{r,g,b}\}}}\; {I_{c}(x)}}},} & (2)\end{matrix}$

where I_(c)(x) is one of the color channels.

The diffuse chromaticity layer can be represented as Λ(x) and thespecular chromaticity layer can be represented as Γ(x). The chromaticitycan then be rewritten as:

I(x)=m _(d)(x)Λ(x)+m _(s)(x)Γ(x),   (3)

where m_(d) and m_(s) are the diffuse and specular reflectioncoefficients, respectively, which can depend on the imaging geometry.

In some embodiments of the invention, the specular chromaticity can beassumed to be uniform for a given image. That is, the red, green andblue channels contribute equally to the specular chromaticity:

Γ_(r)(x)=Γ_(g)(x)=Γ_(b)(x)=1/3.   (4)

Without loss of generality, this can be achieved, for example, bynormalizing the illumination chromaticity estimated from as apreprocessing step.

According to some embodiments of the invention, the specular componentI_(s)(x) can be estimated by first estimating the specular reflectioncoefficient m_(s)(x) from the observed image I(x) and multiplying thespecular reflection coefficient m_(s)(x) by the uniform specularchromaticity Γ. That is, the specular layer can be found from:

I _(s)(x)=m _(s)(x)Γ.   (5)

The dichromatic reflection model in the chromaticity space can berepresented as:

Ĩ(x)=α(x)Λ(x)+(1−α(x))Γ(x)   (6)

where

$\begin{matrix}{\alpha = {\frac{m_{d}}{\left( {m_{d} + m_{s}} \right)}.}} & (7)\end{matrix}$

Using equation (7), the specular reflection coefficient m_(s)(x) can berecovered from

$1 - {\alpha \left( \frac{m_{d}}{\left( {m_{d} + m_{s}} \right)} \right)}$

by the denormalization of intensities:

Σ_(c∈{r,g,b}) I _(c)=Σ_(c∈{r,g,b})(m _(d)Λ+m_(s)Γ)=m _(d) +m _(s).   (8)

From this, the likelihood of the specular layer separation can bewritten as:

E _(D)(α, Λ)=Σ_(x)(Ĩ(x)−(α(x)Λ(x)+(1−α(x))Γ))².   (9)

This likelihood function can then be used in an iterative optimizationproblem to solve for α(x). However, embodiments of the invention includelinear additions to the likelihood function. These can include, forexample, a smoothness component that acts on the specular layer and/oran interior homogeneity component that acts on the diffuse portion.

In some embodiments, the smoothness component can be defined by thegradient of the specular component. The gradient can representsmoothness across edges. FIG. 1C is a visual representation of how thespecular layer is smooth across the image. The image does not includeany sharp changes across the image. This smoothness can be definedmathematically in a number of ways. For instance, the gradient of thechromaticity can be continuous and/or can have a gradual slope in thevector field. This can be represented, for example, by the gradient ofthe specular chromaticity values (1−α(x)). Moreover, in someembodiments, the diffuse reflection can be assumed to be constant on thesame chromaticity in the rg chromaticity space (the red and greenchannels). Thus, in some embodiments, a smoothness likelihood functioncan be defined as:

E _(s)(α)=Σ_(x)∥∇(1−α(x)∥₂,   (10)

where, the gradient,

$\nabla{= {\left( {\frac{\partial\;}{\partial x},\frac{\partial\;}{\partial y}} \right)^{T}.}}$

In some embodiments, the interior homogeneity component of thelikelihood function can act on the diffuse component of the input image.As shown in FIG. 1B the diffuse layer can be assumed to be homogeneouswithin color groups. In this example, the two color panels have the samecolor within each panel. And the color changes abruptly. That is thereis a sharp line between the two panels. A color homogeneity likelihoodfunction that acts on the diffuse layer of the input image can bedefined as:

E _(c)(Λ, λ)=Σ_(x)∥∇Λ_(λ)(x))∥₁+β_(λ)∥λ(x)∥₀,   (11)

where λ={1, . . . , N} denotes the index for a set of chromaticitieswithin the input image and Λ_(λ)(x) returns the chromaticity which Λ(x)indicates. β_(λ)is the weight to control the amount of sparsity on thediffuse chromaticity.

In some embodiments the likelihood functions noted above in equations(9), (10) and (11) can be combined as a linear combination of functions:

E(α, Λ, λ)=E _(D)(α, Λ)+β_(s) E _(s)(α)+B _(c) E _(c)(Λ, λ),   (12)

where and β_(s) and β_(c) are the regularization weights. To ease thecomputational difficulties with this equation, the continuous anddiscrete variables can be uncoupled with an auxiliary variable, suchthat:

E _(c)(Λ, λ, {tilde over (λ)})=Σ_(x)∥∇Λ_(λ)(x)∥₁+β_(λ)∥{tilde over(λ)}(x)∥₀.   (13)

Now, equation (12) can be rewritten as:

$\begin{matrix}{{E\left( {\alpha,\Lambda,\lambda,\lambda} \right)} = {{E_{D}\left( {\Lambda,\alpha} \right)} + {\beta_{s}{E_{s}(\alpha)}} + {\beta_{c}{E_{c}\left( {\Lambda,\lambda,\overset{\sim}{\lambda}} \right)}} + {\frac{1}{2\theta}{\left( {\lambda,{- \overset{\sim}{\lambda}}} \right)^{2}.}}}} & (14)\end{matrix}$

where {tilde over (λ)} is the auxiliary variable for λ of which thesimilarity is controlled by θ. As θ→0 equation (14) becomes equation(12). Equation (14) can be solved for λ and α, to return the specularreflectivity. FIG. 4 outlines an example of a process for solving thisequation. Equation (12) can be used to solve for A and a using anyoptimization algorithm.

In some embodiments of the invention, a dark channel can be used todetermine the diffuse chromaticity and specular chromaticity. This darkchannel can be used to solve any optimization process; for example, theoptimization processes outlined in FIG. 4. Each pixel of the darkchannel image can have the lowest pixel value of the corresponding redchannel pixel, green channel pixel, and blue channel pixel:

I ^(dark)(x)=min_(c∈{r,g,b}) I _(c)(x).   (15)

The dark channel can be used to calculate a pseudo specular-free image:

I _(c) ^(pseudo)(x)=I _(c)(x)−I ^(dark)(x).   (16)

This pseudo specular-free image, created from the dark channel, can beused to initialize any algorithm used to separate specular reflectionsfrom a single image.

Use of a pseudo specular-free image can provide one or more benefits.For example, such an image does not have any ambiguity in the saturationvalue so that color boundaries can be preserved. This property can allowfor accurate separation of the specular reflection in the presence ofcolors ambiguous in saturation value. As another example, this pseudospecular-free image can directly provide specular reflection in case thediffuse reflection of an object has low value in the saturationcomponent.

FIG. 3A shows a pseudo specular image calculated using a conventionaltechnique. FIG. 3B shows a pseudo specular image calculated usingembodiments of the invention. Note that the conventional techniqueregards colors with the same hue but different saturation values asspecular reflection and the technique described herein provides an imagethat does not have the ambiguity in the saturation value. This can helppreserve color boundaries, which can help separate the specularreflection in the presence of colors ambiguous in saturation value.Moreover, the image shown in FIG. 3B can provide specular reflection incase the diffuse reflection of a object has low value in the saturationcomponent.

FIG. 4 shows a process 400 for computing the specular reflectivities fora given image according to some embodiments of the invention. At block405 the dark channel can be computed from the input image. This can bedone, for example, using equation (15). At block 410 a pseudospecular-free image can be determined using the dark channel; forexample, using equation (16). In some embodiments, this pseudospecular-free image can be determined from the normalized image asdiscussed above.

At block 415 the pseudo specular-free image can be clustered intoregions of similar chromaticity. For example, the pseudo specular-freeimage can be clustered based on the color of the regions within theimage. The image can be clustered using any type of cluster analysis.The clustering can return an image (or matrix having the same dimensionas the image) where each pixel indicates an index, λ, representing eachclustered chromaticity. A chromaticity vector, Λ, can also be returnedthat indicates the average chromaticity of each cluster represented byindex, λ. If there are five clusters in the image, then each pixel canbe represented by index, λ, for example, with a number from 1 to 5. Thechromaticity vector, Λ, can then include the five average values of eachchromaticity.

Any type of clustering analysis can be performed. For example,clustering can be performed using k-means clustering, hierarchicalclustering, centroid-based clustering, distributed-based clustering,Lloyd's algorithm, k-medians clustering, the expectation-maximizationalgorithm, density based clustering, linkage clustering, the CLARANSalgorithm, the BIRCH algorithm, and/or canopy clustering.

In some embodiments the clustering can operate on the input image. Insome embodiments this clustering can operate on the pseudo specular-freeimage.

At block 420 cluster indices and chromaticity values can be initialized.For example, initial index λ⁰, with the initial cluster indices Λ⁰ canbe found in block 415. Then, the initial α⁰ can be found by solving:

E _(D)(α, Λ)=Σ_(x)(Ĩ(x)−(α(x)Λ(x)+(1−α(x))Γ))².   (17)

At block 425 these initial values can be used in one or more objectivefunctions. For example, to solve for optimized indices in chromaticityspace, {tilde over (λ)}^(t+1), for fixed α^(t), λ^(t), and Λ^(t), whereinitially t=0, the following objective function can be solved for {tildeover (λ)}^(t+1):

$\begin{matrix}{{\min_{\overset{\sim}{\lambda}}\left\{ {{\beta_{\overset{\sim}{\lambda}}{{\overset{\sim}{\lambda}(x)}}_{0}} + {\frac{1}{2\theta}\left( {{\lambda (x)} - {\overset{\sim}{\lambda}(x)}} \right)^{2}}} \right\}},} & (18)\end{matrix}$

where β_({tilde over (λ)})=β_(c)β_(λ).

-   As another example, to solve for optimized indices space, λ^(t+1),    for fixed α^(t), {tilde over (λ)}^(t), and Λ^(t), the following    objective function can be solved:

$\begin{matrix}{\min_{\lambda}\left\{ {{\beta_{c}\Sigma_{x}{{\nabla{\Lambda_{\lambda}(x)}}}_{1}} + {\frac{1}{2\theta}\left( {{\lambda (x)} - {\overset{\sim}{\lambda}(x)}} \right)^{2}}} \right\}} & (19)\end{matrix}$

And to solve for α^(t+1) and Λ^(t+1) for fixed λ^(t) and {tilde over(λ)}^(t) the following objective function can be solved:

$\begin{matrix}{\min\limits_{\alpha,\Lambda}\left\{ {{\Sigma_{x}\left( {{\overset{\sim}{I}(x)} - \left( {{{\alpha (x)}{\Lambda (x)}} + {\left( {1 - {\alpha (x)}} \right)\Gamma}} \right)} \right)}^{2} + {\beta_{s}\Sigma_{x}{{\nabla\left( {1 - {\alpha (x)}} \right)}}_{2}} + {\beta_{c}\Sigma_{x}{{\nabla{\Lambda_{\lambda}(x)}}}_{1}}} \right\}} & (20)\end{matrix}$

In some embodiments some portions of equation (20) can be left out. Forexample, the function can be computed without the β_(c)Σ_(x)∥∇Λ_(λ)(x)∥₁term. As another example, the function can be computed without theβ_(s)ρ_(x)∥∇(1−α(x)∥₂ term. Various other combinations of objectivefunctions can be used.

With these values in mind, at block 430 it can be determined whether thedifference between consecutive specular layer separation values is lessthan some parameter. For example, this occurs when the differencebetween equation (13) and equation (14) is less than some errorparameter κ.

E(α^(t+1), Λ^(t+1), λ^(t+1), {tilde over (λ)}^(t+1))−E(α^(t), Λ^(t),{tilde over (λ)}^(t))<κ.   (21)

In the event the difference is greater than error parameter κ, thenprocess 400 returns to block 425 and repeats optimization of theobjective function(s) with the new values obtained in the previousiteration.

If the difference is less than error parameter κ, then process 400proceeds to block 435. Using the chromaticity indices λ^(t) and α^(t),the specular chromaticity, I_(s)(x) can be returned using equations (5),(7) and (8).

FIG. 5A shows the diffuse chromaticity component of FIG. 1A and FIG. 5Bshows the specular chromaticity component of FIG. 1A calculated usingembodiments of the invention. The results are consistent with what isshown in FIGS. 1B and 1C.

Embodiments of the invention can be used, for example, in imageprocessing applications to select and edit specular reflections inimages. For example, a user can select a command that initiatesselection of specular reflections of the image. The command can call analgorithm that uses process 200 to find the specular reflections in theimage. If, for example, the user requests that the image of fruit shownin FIG. 2A is processed, then the areas shown as white in FIG. 2B can beselected on the image. For example, the user can then selectively editthese specular reflection portions of the image. As another example, theuser can change the shape, intensity, color, etc. of the portions of theimage having specular reflections.

Embodiments of the invention can be executed on computational system1000 as part of any type of image processing application or otheranother type of application. For instance, embodiments of the inventioncan be used in stereo matching applications. These applications extract3D information from digital images by comparing information about ascene from two vantage points. Because specular reflection changesdepending on the view point, one of the two images may pick up aspecular reflection while the other does not. This can lead tomiscalculations of 3D information. Thus, in stereo matchingapplications, input images can be analyzed for specular reflectivityprior to being used to extract 3D information. Once areas that includespecular reflections have been identified, these areas can be correctedor ignored. For example, these areas can be replaced with averages ofnearby portions of the image. Various other corrections can be used.

As yet another example, embodiments of the invention can be used inimage segmentation applications. Image segmentation is the process ofassigning a label to every pixel in an image such that pixels with thesame label share certain visual characteristics. A specular reflectionwithin an image can show the reflection rather than the color of theobject upon which the reflection occurs. As such the color and/orintensity of pixels representing the specular reflection may not belabeled with the object, which is the object of image segmentation. Thiscan lead to pixels being mislabeled or mis-segmented. Similar problemscan occur in image recognition techniques.

Embodiments of the invention can be used to provide improved specularinformation about an input image. This specular information FIG. 6Ashows the input image shown in FIG. 2A. This image includes specularreflections 205 as noted above. FIG. 6B shows the specular reflectionlayer of FIG. 6A created using embodiments of the invention. FIG. 6Cshows a dark channel image created using embodiments of the invention.This dark channel image can be created, for example, using equation 15.FIG. 6D shows an image representing the specular layer of the inputimage calculated using a conventional technique. Note the differencebetween the image in FIGS. 6B and 6D. In FIG. 6D, the conventionaltechnique improperly considers the background as specular reflection. InFIG. 6B, the image created using embodiments of the invention, most ofthe background is not considered specular. Moreover, FIG. 6D and FIG. 6Care similar to one another. That is, the image created usingconventional technique is very similar to the dark channel image createdusing embodiments of the invention.

FIGS. 7A, 8A and 9A show various examples of an input image withspecular reflection components. FIGS. 7B, 8B and 9B show the specularlayer of the corresponding input image calculated using variousconventional techniques. FIGS. 7C, 8C and 9C show the specular layers ofthe corresponding input images calculated using embodiments of theinvention. As shown, embodiments of the invention more properly specifyspecular components in the input images. For instance, FIGS. 7C, 8C, and9C show less background in the specular layer. And each of these figuresprovides greater contrast between specular and non specular regions.

The computational system 1000, shown in FIG. 10 can be used to performany of the embodiments of the invention. For example, computationalsystem 1000 can be used to execute process 400. As another example,computational system 1000 can be used to perform any calculation,identification and/or determination described here. Computational system1000 includes hardware elements that can be electrically coupled via abus 1005 (or may otherwise be in communication, as appropriate). Thehardware elements can include one or more processors 1010, includingwithout limitation one or more general-purpose processors and/or one ormore special-purpose processors (such as digital signal processingchips, graphics acceleration chips, and/or the like); one or more inputdevices 1015, which can include without limitation a mouse, a keyboardand/or the like; and one or more output devices 1020, which can includewithout limitation a display device, a printer and/or the like.

The computational system 1000 may further include (and/or be incommunication with) one or more storage devices 1025, which can include,without limitation, local and/or network accessible storage and/or caninclude, without limitation, a disk drive, a drive array, an opticalstorage device, a solid-state storage device, such as a random accessmemory (“RAM”) and/or a read-only memory (“ROM”), which can beprogrammable, flash-updateable and/or the like. The computational system1000 might also include a communications subsystem 1030, which caninclude without limitation a modem, a network card (wireless or wired),an infrared communication device, a wireless communication device and/orchipset (such as a Bluetooth device, an 802.6 device, a WiFi device, aWiMax device, cellular communication facilities, etc.), and/or the like.The communications subsystem 1030 may permit data to be exchanged with anetwork (such as the network described below, to name one example),and/or any other devices described herein. In many embodiments, thecomputational system 1000 will further include a working memory 1035,which can include a RAM or ROM device, as described above.

The computational system 1000 also can include software elements, shownas being currently located within the working memory 1035, including anoperating system 1040 and/or other code, such as one or more applicationprograms 1045, which may include computer programs of the invention,and/or may be designed to implement methods of the invention and/orconfigure systems of the invention, as described herein. For example,one or more procedures described with respect to the method(s) discussedabove might be implemented as code and/or instructions executable by acomputer (and/or a processor within a computer). A set of theseinstructions and/or codes might be stored on a computer-readable storagemedium, such as the storage device(s) 1025 described above.

In some cases, the storage medium might be incorporated within thecomputational system 1000 or in communication with the computationalsystem 1000. In other embodiments, the storage medium might be separatefrom a computational system 1000 (e.g., a removable medium, such as acompact disc, etc.), and/or provided in an installation package, suchthat the storage medium can be used to program a general purposecomputer with the instructions/code stored thereon. These instructionsmight take the form of executable code, which is executable by thecomputational system 1000 and/or might take the form of source and/orinstallable code, which, upon compilation and/or installation on thecomputational system 1000 (e.g., using any of a variety of generallyavailable compilers, installation programs, compression/decompressionutilities, etc.) then takes the form of executable code.

Numerous specific details are set forth herein to provide a thoroughunderstanding of the claimed subject matter. However, those skilled inthe art will understand that the claimed subject matter may be practicedwithout these specific details. In other instances, methods, apparatusesor systems that would be known by one of ordinary skill have not beendescribed in detail so as not to obscure claimed subject matter.

Some portions are presented in terms of algorithms or symbolicrepresentations of operations on data bits or binary digital signalsstored within a computing system memory, such as a computer memory.These algorithmic descriptions or representations are examples oftechniques used by those of ordinary skill in the data processing artsto convey the substance of their work to others skilled in the art. Analgorithm is a self-consistent sequence of operations or similarprocessing leading to a desired result. In this context, operations orprocessing involves physical manipulation of physical quantities.Typically, although not necessarily, such quantities may take the formof electrical or magnetic signals capable of being stored, transferred,combined, compared or otherwise manipulated. It has proven convenient attimes, principally for reasons of common usage, to refer to such signalsas bits, data, values, elements, symbols, characters, terms, numbers,numerals or the like. It should be understood, however, that all ofthese and similar terms are to be associated with appropriate physicalquantities and are merely convenient labels. Unless specifically statedotherwise, it is appreciated that throughout this specificationdiscussions utilizing terms such as “processing,” “computing,”“calculating,” “determining,” and “identifying” or the like refer toactions or processes of a computing device, such as one or morecomputers or a similar electronic computing device or devices, thatmanipulate or transform data represented as physical electronic ormagnetic quantities within memories, registers, or other informationstorage devices, transmission devices, or display devices of thecomputing platform.

The system or systems discussed herein are not limited to any particularhardware architecture or configuration. A computing device can includeany suitable arrangement of components that provides a resultconditioned on one or more inputs. Suitable computing devices includemultipurpose microprocessor-based computer systems accessing storedsoftware that programs or configures the computing system from a generalpurpose computing apparatus to a specialized computing apparatusimplementing one or more embodiments of the present subject matter. Anysuitable programming, scripting, or other type of language orcombinations of languages may be used to implement the teachingscontained herein in software to be used in programming or configuring acomputing device.

Embodiments of the methods disclosed herein may be performed in theoperation of such computing devices. The order of the blocks presentedin the examples above can be varied—for example, blocks can bere-ordered, combined, and/or broken into sub-blocks. Certain blocks orprocesses can be performed in parallel.

The use of “adapted to” or “configured to” herein is meant as open andinclusive language that does not foreclose devices adapted to orconfigured to perform additional tasks or steps. Additionally, the useof “based on” is meant to be open and inclusive, in that a process,step, calculation, or other action “based on” one or more recitedconditions or values may, in practice, be based on additional conditionsor values beyond those recited. Headings, lists, and numbering includedherein are for ease of explanation only and are not meant to belimiting.

While the present subject matter has been described in detail withrespect to specific embodiments thereof, it will be appreciated thatthose skilled in the art, upon attaining an understanding of theforegoing, may readily produce alterations to, variations of, andequivalents to such embodiments. Accordingly, it should be understoodthat the present disclosure has been presented for purposes of examplerather than limitation, and does not preclude inclusion of suchmodifications, variations and/or additions to the present subject matteras would be readily apparent to one of ordinary skill in the art.

That which is claimed:
 1. A method for providing a specular reflectivityfrom an input image comprising: receiving the input image at a computerdevice, wherein the input image comprises a red channel, a greenchannel, and a blue channel for each pixel in the input image; computinga cluster analysis on the input image that clusters each pixel in theinput image into clusters having similar chromaticity, wherein thecluster analysis determines a chromaticity index for each pixel and achromaticity vector that indicates an average chromaticity of eachcluster represented by the chromaticity index; determining, from anobjective function, the specular reflectivity of the input image,wherein the objective function includes a function that specifies thatthe specular reflectivity is smooth across edges within the input image;and providing the specular reflectivity of the input image.
 2. Themethod according to claim 1, wherein the objective function specifiesthat a diffuse reflectivity is relatively constant for the samechromaticity.
 3. The method according to claim 1, wherein the objectivefunction specifies that a diffuse reflectivity is relatively constantwithin each cluster.
 4. The method according to claim 1, wherein theobjective function specifies that a diffuse reflectivity changes sharplybetween clusters.
 5. The method according to claim 1, furthercomprising: calculating a dark channel image of the input image, whereinthe dark channel image comprises an image having for each pixel value acorresponding lowest pixel value of the corresponding red channel pixel,green channel pixel, and blue channel pixel of the input image; andcalculating a pseudo specular-free image as a difference between theinput image and the dark channel image, wherein the computing thecluster analysis on the input image comprises computing the clusteranalysis on the pseudo specular-free image.
 6. A non-transitorycomputer-readable storage medium storing computer-executable programinstructions for providing a specular reflectivity from an input image,the program instructions comprising: program code for receiving theinput image at a computer device, wherein the input image comprises ared channel, a green channel, and a blue channel for each pixel in theinput image; program code for computing a cluster analysis on the inputimage that clusters each pixel in the input image into clusters havingsimilar chromaticity, wherein the cluster analysis determines achromaticity index for each pixel and a chromaticity vector thatindicates an average chromaticity of each cluster represented by thechromaticity index; program code for determining, from an objectivefunction, the specular reflectivity of the input image, wherein theobjective function includes a function that specifies that the specularreflectivity is smooth across edges within the input image; and programcode for providing the specular reflectivity of the input image.
 7. Thecomputer-readable storage medium according to claim 6, wherein theobjective function specifies that a diffuse reflectivity is relativelyconstant for the same chromaticity.
 8. The computer-readable storagemedium according to claim 6, wherein the objective function specifiesthat a diffuse reflectivity is relatively constant within each cluster.9. The computer-readable storage medium according to claim 6, whereinthe objective function specifies that a diffuse reflectivity changessharply between clusters.
 10. The computer-readable storage mediumaccording to claim 6, the program instructions further comprising:program code for calculating a dark channel image of the input image,wherein the dark channel image comprises an image having for each pixelvalue a corresponding lowest pixel value of the corresponding redchannel pixel, green channel pixel, and blue channel pixel of the inputimage; and program code for calculating a pseudo specular-free image asa difference between the input image and the dark channel image, whereinthe computing the cluster analysis on the input image comprisescomputing the cluster analysis on the pseudo specular-free image.
 11. Asystem for providing a specular reflectivity from an input image, thesystem comprising: a digital storage device; and a processorcommunicatively coupled to the digital storage device and configured to:receive the input image, wherein the input image comprises a redchannel, a green channel, and a blue channel for each pixel in the inputimage; compute a cluster analysis on the input image that clusters eachpixel in the input image into clusters having similar chromaticity,wherein the cluster analysis determines a chromaticity index for eachpixel and a chromaticity vector that indicates an average chromaticityof each cluster represented by the chromaticity index; store thechromaticity index and the chromaticity vector in the digital storagedevice; solve an objective function to determine the specularreflectivity of the input image; and provide the specular reflectivityof the input image.
 12. The system according to claim 11, wherein theprocessor is further configured to: determine, from the objectivefunction, the specular reflectivity of the input image, wherein theobjective function includes a function that specifies that the specularreflectivity is smooth across edges within the input image.
 13. Thesystem according to claim 11, wherein the objective function specifiesthat a diffuse reflectivity is relatively constant for the samechromaticity.
 14. The system according to claim 11, wherein theobjective function specifies that a diffuse reflectivity is relativelyconstant within each cluster.
 15. The system according to claim 11,wherein the objective function specifies that a diffuse reflectivitychanges sharply between clusters.
 16. The system according to claim 11,wherein the processor is further configured to: calculate a dark channelimage of the input image, wherein the dark channel image comprises animage having for each pixel value a corresponding lowest pixel value ofthe corresponding red channel pixel, green channel pixel, and bluechannel pixel of the input image; and calculate a pseudo specular-freeimage as a difference between the input image and the dark channelimage, wherein the computing the cluster analysis on the input imagecomprises computing the cluster analysis on the pseudo specular-freeimage.